Risk, Return, and
Capital Budgeting
Chapter 12
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• In evaluating projects, all future cash flows are discounted
using a discount rate called cost of capital
• When the cash flow is risk-less, we use the risk-less
discount rate
• When the cash flow is risky, we have to use the discount
rate that takes into account of risk.
• The appropriate discount rate can be computed from the
CAPM Model and the Constant Growth Dividend Model.
• We will first calculate the cost of capital based on two
assumptions:
(1) The firm is all equity financed.
(2) Risk of the project = risk of the whole firm.
• We will relax the assumptions later on.
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The Cost of Equity
• Based on the previous two assumptions, the cost of capital is the
cost of equity.
• Equity Beta:
bS = sSm / sm2
• The Cost of Equity (CAPM):
E(rs) = rf + bs [E(rm) – rf ]
Example:
The following are BCE stocks and TSX300 index returns for
the 1994-1997 period:
Year
BCE
TSX300
1994
4.00%
-0.18%
1995
30.00
14.53
1996
42.00
28.35
1997
34.00
14.98
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Step 1: Calculating the Equity Beta
1)
Calculating average returns:
2)
Calculating the covariance:
3)
Calculating the market variance:
4)
Calculating beta of BCE:
4
Step 2: Calculating the Cost of Equity
• Cost of Equity (CAPM):
Given the current T-bill rate is 5.09% and expected market
return is 14.42%.
Expected market risk premium = 9.33%.
Based on the CAPM, the cost of BCE’s equity is given by:
E(rs) = rf + bBCE [E(rm) - rf]
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An alternative Method for Calculating the Cost of Equity
• In the Chapter 5, we reviewed the constant dividend growth
model.
Dividend
P
1
rs  g
Where rs is the required rate of return of shareholders or the firm’s
cost of equity. g is the growth rate of dividends.
• The above model can be refomulated as
Dividend1
rs 
g
P
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• Example:
The stock price of BCE Inc. is $19.70 per share today. The
dividend is paid annually. The next dividend is $2.50 one
year from now. The expected dividend growth rate is 5%
per year indefinitely. Calculate the cost of equity for BCE.
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The Investment Decision
• Suppose that BCE is an all equity firm. The following are the
expected cash flows for a new project.
Year
CFs (’000)
0
(40,000)
1
5,000
IRR = 13.41%
2
17,000
3
15,000
Calculate NPV and take decision
4
20,000
Assume:
• The BCE Inc. is an all equity firm
• The new project’s beta is the same as BCE’s beta (1.35)
Decision:
• =>. Or:
• Since by the CAPM (SML) the required return for beta of 1.35 is _____, and
IRR=13.41< or > => reject or accept (which one) the new project
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The SML and the Investment Decision
Expected
Return (%)
SML
Whole firm
17.69
IRR = 13.41
New Project
5.09
1.35
Beta
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Determinants of Beta
Factors affecting Equity Beta:
•
Business Risk
1) Cyclicity of Revenues:
•
Typically there are years of good return followed by poor returns.
2) Operating Leverage:
•
•
•
The use of fixed costs in operations may result in magnification of
operating incomes and losses with changes in sales.
Operating leverage increases as fixed costs rise and as variable
costs decline.
Financial Risk
3) Financial Leverage
•
The use of fixed costs in financing (e.g. Once the firm accumulated
debt, the firm must make interest payments regardless of the firm’s
sale)
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Asset Beta and Equity Beta
•
The asset beta is the beta of the assets of the firm.
1)
When the firm is financed with equity only
b ASSET  b EQUITY
2)
When the firm is financed with debt and equity
Debt
Equity
b Debt 
b Equity
Debt  Equity
Debt  Equity
B
S

b Debt 
b Equity
BS
BS
b ASSET 
•
Typically:
b Equity  b ASSET  b Debt
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The Cost of Capital When debt is used
• Assume:
Cost of debt = rB
Cost of equity = rS
• In principal, the cost of capital is the weighted average of rB
and rS . Since the interest payment is a tax deductible expense,
the actual after tax interest cost to the firm is rB (1-Tc)
• The Weighted Average Cost of Capital(WACC):
WACC  rASSETS
S
B
 rs 
 rB  (1  Tc ) 
BS
BS
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Example:
BCE has a debt/equity ratio of 0.4. Assume bs = 0.8; the Tbill rate =4.4%; the market risk premium = 12%; pre-tax
borrowing rate = 10%; the corporate tax rate is 37%.
Calculate the WACC for BCE.
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When the Firm’s beta Differs from the Project’s Beta
• The project and the firm may have different betas
• When the project and the firm are not from the same line of business
• Use industry beta (not always available)
• When the project’s risk is inherently different (even if same industry)
• Estimate the individual project’s beta
• If the project’s risk is higher than the firm’s risk, the project beta
should be used. The higher beta
higher rs
higher rwacc
lower project NPV
• If the project’s risk is lower than the firm’s risk, the project beta
should be used
• Otherwise 2 errors may occur:
• Accept too many high-risk projects
• Reject too many low-risk projects
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